Make a few shallow slashes through the skin of each fillet with a sharp knife, to prevent fillets from curling on the grill. Combine oil, lemon juice, thyme, salt, and pepper. Place fillets in a shallow baking dish and brush with oil mixture. Refrigerate while making relish.

Corn relish: Heat oil in a large skillet over medium-high heat; add corn kernels, red onion, thyme, and garlic and sauté 1 minute. Add vinegar and continue to cook 2 to 3 minutes, until corn is crisp-tender. Remove from heat and stir in remaining relish ingredients.

Heat an outdoor gas grill, or prepare coals for a charcoal grill for direct grilling over medium heat. Heat a nonstick grill pan directly on the grill grate until hot, about 10 minutes. Lightly brush fillets with oil and place flesh side down on grill pan. Grill fish (keeping the grill lid closed as often as possible) until trout is opaque and still moist, 5 to 7 minutes, carefully turning once when fish releases easily from the grill pan. Serve with the corn relish.

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